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Subsampling realised kernels

Author

Listed:
  • Ole E. Barndorff-Nielsen
  • Peter R. Hansen
  • Asger Lunde
  • Neil Shephard

Abstract

In a recent paper we have introduced the class of realised kernel estimators of the increments of quadratic variation in the presence of noise. We showed that this estimator is consistent and derived its limit distribution under various assumptions on the kernel weights. In this paper we extend our analysis, looking at the class of subsampled realised kernels and we derive the limit theory for this class of estimators. We find that subsampling is highly advantageous for estimators based on discontinuous kernels, such as the truncated kernel. For kinked kernels, such as the Bartlett kernel, we show that subsampling is impotent, in the sense that subsampling has no effect on the asymptotic distribution. Perhaps surprisingly, for the efficient smooth kernels, such as the Parzen kernel, we show that subsampling is harmful as it increases the asymptotic variance. We also study the performance of subsampled realised kernels in simulations and in empirical work.

Suggested Citation

  • Ole E. Barndorff-Nielsen & Peter R. Hansen & Asger Lunde & Neil Shephard, 2006. "Subsampling realised kernels," OFRC Working Papers Series 2006fe06, Oxford Financial Research Centre.
  • Handle: RePEc:sbs:wpsefe:2006fe06
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    File URL: http://www.finance.ox.ac.uk/file_links/finecon_papers/2006fe06.pdf
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    References listed on IDEAS

    as
    1. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
    2. Barndorff-Nielsen, Ole E. & Graversen, Svend Erik & Jacod, Jean & Shephard, Neil, 2006. "Limit Theorems For Bipower Variation In Financial Econometrics," Econometric Theory, Cambridge University Press, vol. 22(4), pages 677-719, August.
    3. Kalnina, Ilze & Linton, Oliver, 2006. "Estimating quadratic variation consistently in the presence of correlated measurement error," LSE Research Online Documents on Economics 4413, London School of Economics and Political Science, LSE Library.
    4. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    5. Zhang, Lan & Mykland, Per A. & Ait-Sahalia, Yacine, 2005. "A Tale of Two Time Scales: Determining Integrated Volatility With Noisy High-Frequency Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1394-1411, December.
    6. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2008. "Designing Realized Kernels to Measure the ex post Variation of Equity Prices in the Presence of Noise," Econometrica, Econometric Society, vol. 76(6), pages 1481-1536, November.
    7. Xin Huang & George Tauchen, 2005. "The Relative Contribution of Jumps to Total Price Variance," Journal of Financial Econometrics, Oxford University Press, vol. 3(4), pages 456-499.
    8. Zhou, Bin, 1996. "High-Frequency Data and Volatility in Foreign-Exchange Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 45-52, January.
    9. Aït-Sahalia, Yacine & Mykland, Per A. & Zhang, Lan, 2011. "Ultra high frequency volatility estimation with dependent microstructure noise," Journal of Econometrics, Elsevier, vol. 160(1), pages 160-175, January.
    10. Sílvia Gonçalves & Nour Meddahi, 2009. "Bootstrapping Realized Volatility," Econometrica, Econometric Society, vol. 77(1), pages 283-306, January.
    11. Ole E. Barndorff‐Nielsen & Neil Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280, May.
    12. Oomen, Roel C.A., 2006. "Properties of Realized Variance Under Alternative Sampling Schemes," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 219-237, April.
    13. Zhang, Lan & Mykland, Per A. & Aït-Sahalia, Yacine, 2011. "Edgeworth expansions for realized volatility and related estimators," Journal of Econometrics, Elsevier, vol. 160(1), pages 190-203, January.
    14. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2008. "Designing Realized Kernels to Measure the ex post Variation of Equity Prices in the Presence of Noise," Econometrica, Econometric Society, vol. 76(6), pages 1481-1536, November.
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    More about this item

    Keywords

    Bipower variation; Long run variance estimator; Market frictions; Quadratic variation; Realised kernel; Realised variance; Subsampling.;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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